Trigonometry Examples

$2 (- \frac{\sqrt{226}}{226}) (- \frac{15 \sqrt{226}}{226})$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Move the leading negative in $- \frac{15 \sqrt{226}}{226}$ into the numerator.

$2 (- \frac{\sqrt{226}}{226}) \cdot \frac{- 15 \sqrt{226}}{226}$

Step 1.2

Factor $2$ out of $226$ .

$2 (- \frac{\sqrt{226}}{226}) \cdot \frac{- 15 \sqrt{226}}{2 (113)}$

Step 1.3

Cancel the common factor.

$2 (- \frac{\sqrt{226}}{226}) \cdot \frac{- 15 \sqrt{226}}{2 \cdot 113}$

Step 1.4

Rewrite the expression.

$- \frac{\sqrt{226}}{226} \cdot \frac{- 15 \sqrt{226}}{113}$

Step 2

Multiply $\frac{- 15 \sqrt{226}}{113}$ by $\frac{\sqrt{226}}{226}$ .

$- \frac{- 15 \sqrt{226} \sqrt{226}}{113 \cdot 226}$

Step 3

Raise $\sqrt{226}$ to the power of $1$ .

$- \frac{- 15 ({\sqrt{226}}^{1} \sqrt{226})}{113 \cdot 226}$

Step 4

Raise $\sqrt{226}$ to the power of $1$ .

$- \frac{- 15 ({\sqrt{226}}^{1} {\sqrt{226}}^{1})}{113 \cdot 226}$

Step 5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{- 15 {\sqrt{226}}^{1 + 1}}{113 \cdot 226}$

Step 6

Simplify the expression.

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Step 6.1

Add $1$ and $1$ .

$- \frac{- 15 {\sqrt{226}}^{2}}{113 \cdot 226}$

Step 6.2

Multiply $113$ by $226$ .

$- \frac{- 15 {\sqrt{226}}^{2}}{25538}$

Step 7

Rewrite ${\sqrt{226}}^{2}$ as $226$ .

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Step 7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{226}$ as $226^{\frac{1}{2}}$ .

$- \frac{- 15 {(226^{\frac{1}{2}})}^{2}}{25538}$

Step 7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{- 15 \cdot 226^{\frac{1}{2} \cdot 2}}{25538}$

Step 7.3

Combine $\frac{1}{2}$ and $2$ .

$- \frac{- 15 \cdot 226^{\frac{2}{2}}}{25538}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$- \frac{- 15 \cdot 226^{\frac{2}{2}}}{25538}$

Step 7.4.2

Rewrite the expression.

$- \frac{- 15 \cdot 226^{1}}{25538}$

Step 7.5

Evaluate the exponent.

$- \frac{- 15 \cdot 226}{25538}$

Step 8

Multiply $- 15$ by $226$ .

$- \frac{- 3390}{25538}$

Step 9

Cancel the common factor of $- 3390$ and $25538$ .

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Step 9.1

Factor $226$ out of $- 3390$ .

$- \frac{226 (- 15)}{25538}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $226$ out of $25538$ .

$- \frac{226 \cdot - 15}{226 \cdot 113}$

Step 9.2.2

Cancel the common factor.

$- \frac{226 \cdot - 15}{226 \cdot 113}$

Step 9.2.3

Rewrite the expression.

$- \frac{- 15}{113}$

Step 10

Move the negative in front of the fraction.

$- - \frac{15}{113}$

Step 11

Multiply $- - \frac{15}{113}$ .

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Step 11.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{15}{113})$

Step 11.2

Multiply $\frac{15}{113}$ by $1$ .

$\frac{15}{113}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{113}$

Decimal Form:

$0.13274336 \dots$